Systematic analysis of spectroscopic characteristics of heavy transition metal ions with 4dN and 5dN (N=1…10) electronic configurations in a free state

Systematic consideration of the spectroscopic properties of the di-, tri- and tetravalent 4d and 5d ions in a free state is presented. Variations of the Racah parameters A, B, C, spin-orbit interaction constant ζ and averaged values of the 4d and 5d electrons' radial coordinate across the considered series were considered; functional dependencies between the mentioned quantities were obtained. As a result, knowledge of one out of four parameters (A, B, C, and ζ) allows to estimate the remaining three. The established relations between A, B, C, and ζ reduce the number of independent parameters in the free ion Hamiltonian and can be further applied to the case of crystal-field fitting calculations as the empirical constraints. The third, fourth and fifth ionization energies and barycenters of the electronic 4dN/5dN configurations were calculated; systematic trends across the considered groups of ions were revealed and discussed.